What is meant by heat capacity at constant pressure?

Generally in chemistry and physics, we learned that a material has a heat capacity at constant pressure. However, I am confused at whether this refers to a constant external pressure or a constant system internal pressure?

Staff: Mentor

To elaborate on what BvU said, heat capacity is a physical property of a material, and does not depend on the process being applied to the material. Heat capacity per mole at constant pressure is defined as $$C_p=\left(\frac{\partial H}{\partial T}\right)_P$$
where H is the molar enthalpy of the material. If a process is irreversible so that the internal pressure and temperature of the material are not uniform, this equation still applies locally.